Firstly, in Fig. REF , we show \(C_{9,10}\)  values for parameter sets satisfying
the constraints of neutral meson-antimeson mixings \(\Delta m_K,\Delta m_{B_d},\Delta m_{B_s},\Delta m_D\) , correct relic density \(0.11\le \Omega h^2\le 0.13\)  and \(0< \Delta C_{10}(Z) < 0.79\) ;
here we show region with \(\Delta C_{9}^{\mu \mu }(Z^{\prime }) < 0\)  and \(|\Delta C_{9,10}(Z)|\)  where region
with \(\Delta C_{9}^{\mu \mu }(Z^{\prime }) > 0\)  and \(\Delta C_{9,10} >(<) 0\)  similarly appear.
We find that \(|\Delta C_9(Z)|\)  tends to be small due to suppression factor of \((2 s^2_w - 1/2)\) .
Then the value of \(\Delta C_9^{\mu \mu }\)  can be \(0.83\le -\Delta C_9^{\mu \mu }\le 1.52\)  indicated
by region between dashed line which is obtained from global analysis in Ref. [1]}
(see also Ref. [2]}).
Note that non-zero \(\Delta C_{10}\)  helps to fit \(B_s \rightarrow \mu \mu \)  data.
In fact non-zero \(\Delta C^{ee}_{9,10}(Z)\)  affect the region from global fit but we still use the region
as our reference. We also find that \(C_7\)  is tiny in our allowed region as \(|C_7|< 0.001\)  and
the corresponding plot is omitted.
